/* sf_expm1.c -- float version of s_expm1.c.
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/* sf_expm1.c -- float version of s_expm1.c.
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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*/
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*/
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/*
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/*
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* ====================================================
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* software is freely granted, provided that this notice
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* is preserved.
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* is preserved.
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* ====================================================
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* ====================================================
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*/
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*/
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#include "fdlibm.h"
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#include "fdlibm.h"
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#ifdef __v810__
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#ifdef __v810__
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#define const
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#define const
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#endif
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#endif
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#ifdef __STDC__
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#ifdef __STDC__
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static const float
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static const float
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#else
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#else
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static float
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static float
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#endif
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#endif
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one = 1.0,
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one = 1.0,
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huge = 1.0e+30,
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huge = 1.0e+30,
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tiny = 1.0e-30,
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tiny = 1.0e-30,
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ln2_hi = 6.9313812256e-01,/* 0x3f317180 */
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ln2_hi = 6.9313812256e-01,/* 0x3f317180 */
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ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */
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ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */
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invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */
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invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */
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/* scaled coefficients related to expm1 */
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/* scaled coefficients related to expm1 */
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Q1 = -3.3333335072e-02, /* 0xbd088889 */
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Q1 = -3.3333335072e-02, /* 0xbd088889 */
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Q2 = 1.5873016091e-03, /* 0x3ad00d01 */
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Q2 = 1.5873016091e-03, /* 0x3ad00d01 */
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Q3 = -7.9365076090e-05, /* 0xb8a670cd */
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Q3 = -7.9365076090e-05, /* 0xb8a670cd */
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Q4 = 4.0082177293e-06, /* 0x36867e54 */
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Q4 = 4.0082177293e-06, /* 0x36867e54 */
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Q5 = -2.0109921195e-07; /* 0xb457edbb */
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Q5 = -2.0109921195e-07; /* 0xb457edbb */
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#ifdef __STDC__
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#ifdef __STDC__
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float expm1f(float x)
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float expm1f(float x)
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#else
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#else
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float expm1f(x)
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float expm1f(x)
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float x;
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float x;
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#endif
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#endif
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{
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{
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float y,hi,lo,c,t,e,hxs,hfx,r1;
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float y,hi,lo,c,t,e,hxs,hfx,r1;
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__int32_t k,xsb;
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__int32_t k,xsb;
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__uint32_t hx;
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__uint32_t hx;
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GET_FLOAT_WORD(hx,x);
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GET_FLOAT_WORD(hx,x);
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xsb = hx&0x80000000; /* sign bit of x */
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xsb = hx&0x80000000; /* sign bit of x */
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if(xsb==0) y=x; else y= -x; /* y = |x| */
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if(xsb==0) y=x; else y= -x; /* y = |x| */
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hx &= 0x7fffffff; /* high word of |x| */
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hx &= 0x7fffffff; /* high word of |x| */
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/* filter out huge and non-finite argument */
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/* filter out huge and non-finite argument */
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if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */
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if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */
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if(FLT_UWORD_IS_NAN(hx))
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if(FLT_UWORD_IS_NAN(hx))
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return x+x;
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return x+x;
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if(FLT_UWORD_IS_INFINITE(hx))
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if(FLT_UWORD_IS_INFINITE(hx))
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return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
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return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
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if(xsb == 0 && hx > FLT_UWORD_LOG_MAX) /* if x>=o_threshold */
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if(xsb == 0 && hx > FLT_UWORD_LOG_MAX) /* if x>=o_threshold */
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return huge*huge; /* overflow */
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return huge*huge; /* overflow */
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if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
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if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
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if(x+tiny<(float)0.0) /* raise inexact */
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if(x+tiny<(float)0.0) /* raise inexact */
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return tiny-one; /* return -1 */
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return tiny-one; /* return -1 */
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}
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}
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}
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}
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/* argument reduction */
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/* argument reduction */
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if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
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if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
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if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
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if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
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if(xsb==0)
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if(xsb==0)
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{hi = x - ln2_hi; lo = ln2_lo; k = 1;}
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{hi = x - ln2_hi; lo = ln2_lo; k = 1;}
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else
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else
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{hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
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{hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
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} else {
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} else {
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k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
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k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
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t = k;
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t = k;
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hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
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hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
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lo = t*ln2_lo;
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lo = t*ln2_lo;
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}
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}
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x = hi - lo;
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x = hi - lo;
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c = (hi-x)-lo;
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c = (hi-x)-lo;
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}
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}
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else if(hx < 0x33000000) { /* when |x|<2**-25, return x */
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else if(hx < 0x33000000) { /* when |x|<2**-25, return x */
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t = huge+x; /* return x with inexact flags when x!=0 */
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t = huge+x; /* return x with inexact flags when x!=0 */
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return x - (t-(huge+x));
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return x - (t-(huge+x));
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}
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}
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else k = 0;
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else k = 0;
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/* x is now in primary range */
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/* x is now in primary range */
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hfx = (float)0.5*x;
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hfx = (float)0.5*x;
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hxs = x*hfx;
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hxs = x*hfx;
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r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
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r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
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t = (float)3.0-r1*hfx;
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t = (float)3.0-r1*hfx;
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e = hxs*((r1-t)/((float)6.0 - x*t));
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e = hxs*((r1-t)/((float)6.0 - x*t));
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if(k==0) return x - (x*e-hxs); /* c is 0 */
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if(k==0) return x - (x*e-hxs); /* c is 0 */
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else {
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else {
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e = (x*(e-c)-c);
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e = (x*(e-c)-c);
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e -= hxs;
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e -= hxs;
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if(k== -1) return (float)0.5*(x-e)-(float)0.5;
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if(k== -1) return (float)0.5*(x-e)-(float)0.5;
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if(k==1) {
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if(k==1) {
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if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
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if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
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else return one+(float)2.0*(x-e);
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else return one+(float)2.0*(x-e);
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}
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}
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if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
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if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
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__int32_t i;
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__int32_t i;
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y = one-(e-x);
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y = one-(e-x);
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GET_FLOAT_WORD(i,y);
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GET_FLOAT_WORD(i,y);
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SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
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SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
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return y-one;
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return y-one;
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}
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}
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t = one;
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t = one;
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if(k<23) {
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if(k<23) {
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__int32_t i;
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__int32_t i;
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SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
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SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
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y = t-(e-x);
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y = t-(e-x);
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GET_FLOAT_WORD(i,y);
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GET_FLOAT_WORD(i,y);
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SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
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SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
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} else {
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} else {
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__int32_t i;
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__int32_t i;
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SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */
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SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */
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y = x-(e+t);
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y = x-(e+t);
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y += one;
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y += one;
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GET_FLOAT_WORD(i,y);
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GET_FLOAT_WORD(i,y);
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SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
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SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
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}
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}
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}
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}
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return y;
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return y;
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}
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}
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#ifdef _DOUBLE_IS_32BITS
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#ifdef _DOUBLE_IS_32BITS
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#ifdef __STDC__
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#ifdef __STDC__
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double expm1(double x)
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double expm1(double x)
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#else
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#else
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double expm1(x)
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double expm1(x)
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double x;
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double x;
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#endif
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#endif
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{
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{
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return (double) expm1f((float) x);
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return (double) expm1f((float) x);
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}
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}
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#endif /* defined(_DOUBLE_IS_32BITS) */
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#endif /* defined(_DOUBLE_IS_32BITS) */
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